Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

By Frank Verstraete, V. Murg, J. I. Cirac. 2008

1,604 citations recorded by the source corpus.

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/1e9d3284973d2a09011b06f3ba9be722e7ce2f66

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “The linear growth of the entanglement entropy in time is also a very important physical phenomenon to understand why algorithms based on matrix product states [91] (such as the density matrix renormalisation group [92] in its time dependent version [93] or iTEBD [94]) fail to describe the quench dyn”
Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains (2014, background): “A general discussion of tensor networks and their use in numerical simulations for quantum spin systems can be found in [71,72].”
Dynamics of non-Markovian open quantum systems (2015, background): “…non-Markovianity as a resource to build the desired quantum state may open new avenues for developing further the concept of dissipative quantum computation and state preparation proposed in (Diehl et al., 2008, 2010; Verstraete et al., 2008) and experimentally realized in (Subasi et al., 2012).”
Quantum spin liquid states (2016, background): “Readers can refer to references (Cirac and Verstraete, 2009; Orus, 2014; Verstraete et al., 2008) for details.”
Quantum information processing with superconducting circuits: a review (2016, background): “Advanced approximations can be constructed via coupledcluster (CC) [394] or matrix product (MPS) [395] reference states.”
Towards quantum machine learning with tensor networks (2018, background): “matrix renormalization study of the hubbard model [4]on a bethe lattice,” The European Physical Journal B - Con-”
Random Quantum Circuits (2022, background): “The minimal cut is a way of bounding entanglement in any tensor network (150, 151, 152, 153, 154).”
The mass spectrum of the Schwinger model with matrix product states (2013, methodology): “e practically indistinguishable at the scale of the plots. The ﬁnal values for the binding energies, M V g , and their errors (see Appendix A) are displayed under the corresponding plots. PEPS ansatz [13, 40]. Algorithms exist for the ground state search and for simulating the evolution also in the ”
Quantum Entanglement Growth Under Random Unitary Dynamics (2016, methodology): “Entanglement growth is also of practical importance as the crucial obstacle to simulating quantum dynamics numerically, for example using matrix product states or the Density Matrix Renormalization Group (DMRG) [21].”
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, background): “…and nonequilibrium 1D systems (Schollwöck, 2005; Schollwöck and White, 2006; Vidal, 2003, 2004; White, 1992) and higher dimensional ones (Verstraete et al., 2008), the Keldysh technique (Kamenev and Levchenko, 2009) which is particularly helpful for deriving quantum kinetic equations,…”